(2020) Modeling of gas-phase heterogeneous photocatalytic oxidation reactor in the presence of mass transfer limitation and axial dispersion

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Chemical Engineering Journal
journal homepage: www.elsevier.com/locate/cej
Modeling of gas-phase heterogeneous photocatalytic oxidation reactor in the
presence of mass transfer limitation and axial dispersion
Mojtaba Malayeria, Chang-Seo Leea, Fariborz Haghighata,⁎, Lubomir Klimesb
a Energy and Environment Group, Department of Building, Civil and Environmental Eng., Concordia University, Montreal, Canada
b Sustainable Process Integration Laboratory, Brno University of Technology, Brno, Czech Republic
H I G H L I G H T S
• Modeling of UV-PCO was performed under mass transfer limitation and axial dispersion.
• CFD simulation was used to determine the flow distribution.
• RTD analysis was conducted to determine dispersion in the reactor.
• A mass balance equation was used to find mass transfer coefficient in a fibrous catalyst.
• A correlation for Sherwood number at low Reynolds number was proposed.
A R T I C L E I N F O
Keywords:
UV-PCO reactor
Air purification
CFD analysis
Residence time distribution
Mass transfer coefficient
Sherwood number
A B S T R A C T
Mass transfer plays a critical role in the efficiency of photocatalytic oxidation (PCO) technology for air pur-
ification applications. There has been limited work on the exploration of mass transfer in the PCO reactor with
the non-ideal flow. In this work, the performance of a continuous heterogeneous ultraviolet photocatalytic
oxidation (UV-PCO) reactor was investigated and addressed under mass transfer limitation and axial dispersion.
First, CFD modeling was used to determine the flow distribution in the reactor at various airflow rates. The
residence time distribution (RTD) analysis with a tracer gas (CO2) was carried out for the experimental vali-
dation of the simulation model and good agreement between experimental and simulation data was achieved.
Further, a quick and straightforward methodology employing an axial dispersion plug flow model was used to
study the RTD. The proposed model could predict the residence time distribution of CO2 with high accuracy.
Results of the RTD for CO2 in the presence and absence of a PCO filter (silica fiber felts (SFF) modified with TiO2)
were almost identical due to the high porosity of the filter. The model was then used for the evaluation of the
axial dispersion of methyl ethyl ketone (MEK) at different flow rates. Owing to a low value of the Peclet number
(Pe < 100), the flow in the reactor deviated from an ideal plug flow and dispersion could not be ignored. The
photocatalysis reaction of MEK by the SFF filter under the mass-transfer-controlled regime was further ad-
dressed. A steady-state mass balance equation was implemented for the assessment of the performance of the
UV-PCO reactor in the presence of axial dispersion and mass transfer limitation. The mass transfer coefficient
was calculated with the use of the developed model and a correlation for the Sherwood number was proposed to
relate the mass transfer coefficient to the flow rate and fiber structure. The proposed correlation was assessed
and compared with the other empirical formulas available in the literature.
1. Introduction
Ultraviolet photocatalytic oxidation (UV-PCO) has been acclaimed
to be an efficient and viable technology for air purification [1]. In this
emerging technology, a semiconductor, mostly TiO2, is used as a pho-
tocatalyst and UV lamps are applied as an energy source for the creation
of electron/hole pairs. Generated charge carriers, in the presence of
water and oxygen, form highly oxidizing agents such as hydroxyl ra-
dical, which can result in degradation of organic compounds adsorbed
on the surface through a series of photochemical reactions. The ad-
vantages of PCO include low operating temperature, low cost and re-
latively low energy consumption [2–4].
There are several types of photoreactors reported in the literature,
such as flat plate [5,6], annular [7,8], packed bed [9,10] and monolith
https://doi.org/10.1016/j.cej.2020.124013
Received 12 October 2019; Received in revised form 21 December 2019; Accepted 1 January 2020
⁎ Corresponding author.
E-mail address: Fariborz.Haghighat@concordia.ca (F. Haghighat).
Chemical Engineering Journal 386 (2020) 124013
Available online 03 January 2020
1385-8947/ © 2020 Elsevier B.V. All rights reserved.
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[11,12], which were developed for air remediation by UV-PCO. Gen-
erally, an efficient reactor requires high surface area, low air velocity
and direct light radiation to the reaction surface [13]. Numerous ex-
perimental and modeling studies have been dedicated to the analysis of
PCO performance, and a comprehensive literature review on modeling
various PCO reactors is available [14]. Photocatalytic reactors are often
different from ideal reactors like batch, perfect mixed, and plug flow
reactors. Most previous studies assumed idealized plug flow or perfectly
mixed reactors, where all the flow elements in the reactor have the
same residence time [15]. Therefore, evaluation of residence time dis-
tribution (RTD) for flow regimes is one of the most informative char-
acterizations of photoreactor. RTD analysis provides key information
for successful design, modeling, scale-up, and enables us to evaluate if
PCO reactors can be simulated as ideal systems, like ideal perfect mixed
and ideal plug flow reactors [16,17].
Computational fluid dynamics (CFD) is also a powerful tool for the
understanding of flow characteristic within the reactor [18]. It is an
approach based on the numeric solution of governing equations for
fluid motion, which considers the actual geometrical design of the re-
actor and all characteristics of the airflow [19]. Mohseni and Taghipour
[20] utilized CFD to provide a deeper understanding of the flow dis-
tribution in a continuous annular UV photocatalytic reactor. The CFD
modeling was performed considering a laminar flow. This assumption
of laminar flow caused about 10–20% underestimation of the de-
gradation rate. In another study by Sozzi and Taghipour [21], the
turbulent flow through two different characteristic UV-reactor config-
urations was numerically investigated. The simulation results showed a
close agreement with the experimental data for both reactors by con-
sidering an appropriate mesh structure and turbulence model. The va-
lidated CFD model could signify the influences of reactor configuration
and internal reactor structures on the flow distribution. Salvado-Estivill
et al. [5] performed a CFD simulation of a narrow-slit, flat-plate, single-
pass, flow-through photocatalytic reactor for air purification using 2D
and 3D modeling. Both models were shown to approximate the ex-
perimental results of the oxidation of trichloroethylene (TCE) closely,
while the 2-D model is a more straightforward and less time-consuming
approach.
To predict the performance of a photocatalytic reactor, it is neces-
sary to obtain the kinetic reaction rate constants. This requires using a
reactor operating in a regime in which mass transfer limitations are not
significant, for instance, in a well-mixed batch reactor. In such a case,
the kinetic parameters are independent of the reactor configuration
[22,23]. However, mass transfer limitations have a prominent role in
the reaction rate of continuous PCO systems. In a photocatalytic reac-
tion, the catalyst is typically in a different phase from the reactants.
Accordingly, the degradation rate is mainly depended on the mass
transfer between these phases [24]. Tomasic et al. [25] investigated the
impact of critical parameters on the behavior of the annular photo-
catalytic reactor through plug flow and laminar flow modeling.
The
simulation result showed that the performance of the photoreactor is
primarily limited by the inter-phase mass transfer. Vezzoli et al. [26]
developed a model for photocatalytic oxidation of phenol in a flat plate
reactor to study the influence of various reaction parameters. Specific
attention was given to the mass transfer phenomena and the impact of
TiO2 film thickness. They observed that the reaction is external mass
transfer limited, even at the highest flow rate, while internal diffusion
phenomena have a negligible effect due to the small thickness of the
catalyst film.
One of the possible ways to minimize mass transfer resistance is the
application of new geometrical forms of catalysts, characterized by low
pressure drop and, simultaneously, with higher mass transfer efficiency.
Among various new types of catalysts, using catalysts on fibrous sup-
ports, e.g., glass fiber catalysts (GFCs), is very promising as the mass
transfer is influenced by the structure of fibers [27]. Zagoruiko et al.
[28] examined various fibrous catalysts to investigate the impact of
different structural elements on the rate of mass transfer. They found
out that catalysts with a higher flexibility of fibrous supports, due to
more efficient flow turbulization, has a higher mass transfer rate.
Although substantial research work has been published on the
modeling of the PCO reactor for air purification, most of the existing
models were verified based on small scales under ideal conditions
[3,29]. In the small-scale reactors, the plug flow model and laminar
velocity profile (with negligible dispersion) could describe flow beha-
vior and mass transfer in the reactor. However, an appropriate de-
scription of the hydrodynamics is necessary to consider fluid mixing,
mass transfer from the gas phase to solid phase and reaction at the
catalyst surface for proper evaluation of reaction rate. This is increas-
ingly more important when simulating large-scale reactors, in which
Nomenclature
English symbols
as geometric surface area per unit volume, (m2/m3)
C Concentration in gas phase, (mg/m3)
C inj0, Time-dependent tracer concentration, (mg/m3)
Cin Inlet concentration, (mg/m3)
Cout Outlet concentration, (mg/m3)
Cs Concentration in catalyst phase, (mg/m3)
d Fiber diameter (m)
Dax Axial dispersion coefficient, (m2/s)
Dm Molecular diffusion coefficient, (m2/s)
kapp Apparent reaction rate constant, (1/s)
km ext, External mass transfer coefficient, (m/s)
kov Overall reaction rate constant, (1/s)
L Reactor length, (m)
Lf Thickness of filter, (m)
Lfb Length of fiber, (m)
Q Flow rate, (L/min)
r Reaction rate, (mg/m3.s)
t Time (s)
td Time delay (s)−
tm Mean residence time, (s)
u Superficial velocity, (m/s)
ub Interstitial velocity (m/s), = εu u/b
Greek letters
σ Variance of the residence time
σθ Dimensionless variance
ε Bed porosity
δ Time interval, (s)
δf TiO2 layer thickness, (m)
νt Turbulent kinematic viscosity, (m2/s)
ϑ Air dynamic viscosity, (m2/s)
τ Hydraulic residence time, (s)
Dimensionless parameters
E Residence time distribution function
Pe Peclet number, Pe = uL/Dax
Re Reynolds number, = εRe u d/ ϑb
Sc Schmidt number, =Sc ϑ/Dm
Sh Sherwood number, =Sh k d/Dm,ext m
X Removal efficiency
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
2
dispersion, bypass, recirculation, and dead zone may happen and the
effect of fluid elements containing different velocities cannot be ignored
[30,31]. Therefore, the performance of existing PCO models validated
for small scale could be questionable and may not be scaled up to si-
mulate the full-scale reactors correctly [3]. Moreover, most of the
correlations for the mass transfer coefficient were obtained for non-
photocatalyst media with larger characteristic length. Nevertheless, in
fiberglass-based PCO filter, the characteristic length is very small (due
to micro-size of fiber), and consequently, Reynolds number is quite low.
This can cause a considerable deviation when a mass transfer correla-
tion validated for non-fiber is used for fiber one. This paper presents a
modeling study on the photocatalytic oxidation of methyl ethyl ketone
(MEK) by SFF modified with titanium dioxide as a photocatalyst when
the kinetic reaction rate does not control the system (very fast reaction).
First, a three-dimensional CFD modeling has been conducted to simu-
late the behavior of flow in the photochemical reactor. An accurate CFD
model can provide greater insight into the evaluation of the velocity
profile on the PCO filter. Since airflow in the continues system deviates
from ideal flow, a residence time distribution (RTD) analysis with tracer
gas is then performed to find a quantitative characterization of the
carrier fluid hydrodynamics and its divergence from ideal conditions.
The experimental data were compared to the CFD simulation results.
Moreover, an axial dispersion plug flow model was proposed to re-
present the residence time distribution of the challenge compounds in
the reactor. Finally, this paper focuses on the modeling of the PCO
reactor under mass transfer-controlled regime. A mass transfer corre-
lation (Sherwood formula) for the SFF filter in the UV-PCO reactor was
proposed and compared with the results of other existing ones in the
literature.
2. Methodology
The application of the PCO technique was restricted to controlled
laboratory experiments. Hence, the simulation model needs to be va-
lidated to extend its applicability. The experimental validation of the
model provides an accurate and credible PCO model, which makes it
possible to be used in a larger scale without the need to conduct costly
experimental measurements.
The present study focuses on two main sections; experiment and
modeling. In order to validate the model and to estimate the unknown
parameters, some experiments have been conducted in a bench-scale
reactor. Modeling of the reactor was performed using both CFD simu-
lation and 1-D axial dispersion plug flow model, which are explained in
more detail later.
2.1. Experimental setup
Fig. 1 depicts the experimental set-up used to study the photo-
catalytic oxidation performance of MEK on TiO2 coated SFF. The pho-
tocatalytic reactor is an aluminum duct with 10 cm × 10 cm inner cross-
section area and 1.3 m length in order to provide a uniform flow.
Compressed air, with a relative humidity of 0% and temperature
around 20 °C, is used as the carrier gas and its flow rate was controlled
by a mass flow meter (OMEGA, FMA5542A). In this study, the flow rate
was varied from 10 to 40 L/min. The inlet air humidity was adjusted via
passing a portion of compressed air to a bubbling system filled with
distilled water. In this study, the relative humidity in the reactor was
23±1%. The challenge compound was automatically injected through a
syringe pump (KD Scientific, Model KDS-210) into the airflow. The
temperature and humidity were monitored using a sensor (DATAQ In-
struments, Model EL-USB-2). 2 UV lamps (Philips, TUV PL-S 5 W/4P),
at each site of PCO filter, were installed to deliver more efficient UV
energy to TiO2.
2.2. Analysis instruments
The air was monitored using the Fluke 975 AirMeter for CO2, and
PID detector (ppb3000 RAE) for TVOC in the tracer signal injection test
(RTD experiment). Perkin Elmer High Performance Liquid
Chromatography (HPLC) was used to analyze the MEK in the PCO re-
action test. The target compound was absorbed on a high purity silica
adsorbent coated with 2, 4-dinitrophenylhydrazine (2, 4-DNPH) car-
tridge, the absorbed compound was extracted with acetonitrile based
on US EPA TO-11a [32]. Furthermore, in the PCO reaction test, the
concentration of the pollutant at downstream of the reactor was con-
tinuously recorded by a PID detector during the initial dark adsorption
step to find the filter breakthrough point.
Fig. 1. Schematic diagram of the experimental set-up for PCO experiments.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
3
2.3. Modeling with COMSOL Multiphysics
In the present
study, modeling in COMSOL Multiphysics (from
COMSOL Inc.) was performed in two stages; first, a steady-state tur-
bulent flow study within the reactor, and second, a tracer study (RTD
analysis) with a solution of mass balance including the flow distribution
from the first stage but considering unsteady conditions (transient si-
mulation).
The simulation of airflow in the PCO reactor was conducted using
the CFD module of COMSOL, which is a commercial finite-element-
method-based modeling tool. Even though the fluid flow through the
main part of the reactor is laminar, the value of Reynolds number at the
entrance region was high in the bench-scale system using compressed
air, representing a turbulent regime. Due to this complexity, the use of
an appropriate model allowing for consideration of turbulence effects is
crucial. Various turbulent models are available in COMSOL, such as k-ε
and k-ω. The k-ε model is the most widely-used engineering turbulence
model [33]. This model is quite robust, economical, and reasonably
accurate in a wide range of flow conditions. However, it is suitable
rather for external flows, is accurate only in the fully turbulent regime
and some difficulties can occur in complex 3-D cases. Moreover, the k-ε
model tends to over predict turbulence generation in regions where the
flow is highly accelerated or decelerated [21]. On the other hand, the k-
ω model is often more suitable in cases where the k-ε model is not
accurate, such as with internal flows in non-circular ducts. Moreover,
the k-ω model possesses high accuracy and applicability when used in
regions with the laminar flow for which the turbulent kinetic energy
becomes zero [34]. Due to these reasons, the k-ω turbulence model was
applied in this study to simulate the fluid flow in the PCO reactor. The
reasons for using the turbulent model can be expressed as follows:
1) The straight inlet pipe with a diameter of 6 mm was considered in
the model to simulate turbulent effects inside a flexible hose. The flow
in the inlet pipe was turbulent due to a small diameter of the hose and
high air velocity through it.
2) The wire mesh located near the inlet of the reactor for the airflow
homogenization caused a local reduction of the cross-section of the
reactor. Such reduction necessitates an increased air velocity, resulting
in a locally increased Reynolds number corresponding to the turbulent
flow. Moreover, the fluid flow pattern in the vicinity and behind the
wire mesh was, in general, expected to be more complex and rather
turbulent.
The fluid flow was solved in COMSOL Multiphysics 5.1 as an in-
compressible flow with the k- ω model, which was the two-equation
turbulence model adopting the Wilcox revised model [35] with realiz-
ability constraints, and the Reynolds-averaged Navier–Stokes (RANS)
approach. The internal geometry of the reactor was created in COMSOL
as a geometry node. Then, due to its symmetry, the geometry was di-
vided longitudinally in half to save computational resources. The lateral
face (longitudinal cut) was set to a symmetry boundary condition. The
boundary conditions of the internal walls of the reactor were treated
with a built-in procedure employing wall functions. A uniform velocity
profile u0 at the inlet and zero gauge pressure (meaning the atmo-
spheric pressure) at the outlet were specified.
The mesh used in the simulations consisted of mainly tetrahedral
and swept elements. The influence of the mesh density to simulation
results was investigated by means of eight various mesh configurations.
It was necessary to create a sufficiently dense mesh near the entrance of
the reactor and the wire mesh where large velocity gradients and vor-
texes can exist. The finest considered mesh contained about 8.1 million
of elements, while the coarsest one consisted of 0.31 million of mesh
elements. The mesh independence and the suitable mesh configuration
was evaluated and identified, respectively, by refining the mesh until
the velocity profile was affected less than 1% by a further refinement.
The mesh with 2.36 million elements with an average element quality
of 0.71 was determined as suitable in this respect (more details can be
found in the Supporting information file). The mesh generation process
was made by considering the maximum element size, minimum ele-
ment size, element growth rate, and curvature factor 5.7, 1.1, 1.13, and
0.5, respectively. At the entrance section (including the expansion in
the geometry of the duct and the wire mesh), at the middle part of the
reactor (where the lamps are placed), and at the outlet, the tetrahedral
type of mesh elements was used. In other sections of the reactor, where
the geometry of the duct has a simple geometry, the swept mesh (prism
mesh elements) was adopted.
In the next stage, a tracer study (RTD analysis) was performed by
means of the solution of mass balance in the time-domain. As the tracer
was present in a diluted form, a COMSOL built-in model for transport of
diluted species from Chemical Reaction Engineering Module was ap-
plied. This model allows for the solution of diffusion and convection
and for modeling the component concentration in the fluid. In the ad-
vection–diffusion mode, the turbulent kinematic viscosity νt was used as
the turbulent diffusivity in the mass balance equation [36]. The tracer
concentration over time at the inlet of the reactor (the input signal) was
defined as follows [36,37]:
= − −C C t texp( ( ) )in inj d0, 2 (1)
where td stands for the time delay during the injection (in the present
paper, =t s4d was applied).
The simulation was conducted with an insulation boundary condi-
tion (no-flux) and also advective flux specified as boundary conditions
at the internal walls and the outlet, respectively. For the outlet con-
centration, it was assumed that mass transfer was only caused due to
convection in the free-flowing fluid. A summary of the boundary con-
ditions is presented in Table 1.
2.4. Material
A commercial PCO filter (Saint-Gobain Quartzel TiO2 photocatalyst)
was used in this research, which is composed of long, continuous
amorphous silica fiber felts modified with TiO2 (TiO2/SFF). Table 2
gives the technical data, including BET surface area, bed porosity,
thickness, etc. The morphology of the PCO filter surface was de-
termined by Scanning Electron Microscopy (SEM) system (Hitachi
Tungsten Filament S-3400 N Variable Pressure SEM). Fig. 2a–c presents
the SEM images of TiO2 coated on silica fiber felts filter at different
magnifications. BET surface area and pore parameters of the PCO filter
were estimated by N2 adsorption measurement (Quantachrome, Auto-
sorb-1). Methyl ethyl ketone (99.9%) was used as target VOC and
acetonitrile (HPLC grade) for HPLC analysis, was purchased from Fisher
Scientific Inc. (ON, Canada). Ultra-high purity (99.99%) carbon dioxide
was provided from Air Liquid Canada Inc. as a tracer gas for residence
time distribution (RTD) analysis.
2.5. Residence time distribution experiment
To characterize the flow in the PCO reactor, the Residence Time
Distribution (RTD) was determined by the injection of carbon dioxide
(CO2) and methyl ethyl ketone (MEK) tracers into the process fluid
(air). The CO2 tracer gas was used to evaluate the effect of SFF filter on
RTD since it is an inert passive gas that is adsorbed little on the pho-
tocatalyst. The RTD experiment with MEK (as a target compound for
the PCO reaction) for flow rates, ranging from 10 L/min to 40 L/min,
was also performed to determine the axial dispersion coefficient. In
order to verify the applicability of the result, RTD test was also
Table 1
Boundary conditions for the CFD model.
Inlet Outlet Channel wall
Momentum balance u0 p0 Wall function
Component mass balance Cin Convective flux No flux
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
4
conducted at flow rates of 50 L/min and 60 L/min.
An input signal of 1 mL of CO2 was loaded instantly into the inflow
stream, using a syringe at time t = 0 s (flow
rate of 10 L/min). CO2
outlet concentrations were measured as a function of time using a CO2
analyzer (Fluke 975 AirMeter) (Fig. 3). In the case of MEK tracer signal
(input signal of 1 uL), its outlet concentrations were measured in time
for various flow rates by a PID detector (ppb3000 RAE). The exit age
distribution function, E(t) is defined as follows [38]:
∫
=
=
=
∑
∞
∞
E t C t
C t dt
C t
C t δ t
( ) ( )
( )
Tracer concentration in the outlet at time t
Total area under tracer concentration curve versus time
( )
( ) ( )
i
i i
0
0 (2)
It should be noted that for CO2 testing, the RTD experiment was
performed in presence of PCO filter, due to the non-adsorptive char-
acteristic of CO2 on the media while MEK testing was carried out
without the filter (as shown in Fig. 3).
2.6. Mass-transfer limited PCO experiment
Experimental conditions for the mass transfer-controlled regime in
the PCO reactor include the use of high light intensity and an extremely
active photocatalyst. Moreover, short residence time is necessary to
limit the conversion. This can be accomplished by means of high flow
rates. In this study, the PCO filter with thicknesses of 3 mm and 5 mm,
and the MEK concentration of 150 ppb were utilized. A low challenge
concentration was chosen to achieve a high conversion of the oxidation
reaction at a lower level of light intensity. In order to investigate the
mass transfer rate effect on the performance, it is more favorable to
operate at high conversions, since the efficiency reduction with flow
rate increment can be observed clearer than at low conversions. To
ensure that the photocatalyst was operating in the mass transfer limited
regime, experiments at various light intensities (26, 52, 78, and
104 mW/cm2) were carried out to determine the independency of the
MEK removal efficiency on the light intensity. Further, the experiments
in the second series were performed for a constant intensity (78 mW/
cm2) with the variation of the gas flow rate in the range of 10–40 L/
min.
3. Result and discussion
3.1. CFD simulations
In the steady-state analysis, the CFD model provided the velocity
distribution throughout the flow domain. Numerical results demon-
strate that the velocity distribution through the reactor, particularly, at
the entrance, after and behind the wire mesh, and also in the reaction
section is non-uniform (see Fig. 4). The simulations were performed for
various airflow rates, the range of 10–40 L/min, to investigate fluid
dynamics in the photocatalytic reactor. Fig. 5 shows the distribution
and contours of the velocity magnitude at the filter cross-section for
various flow rates. It is clear from the figure that the lamp has a major
impact on the flow distribution on the filter. However, the velocity at
the lower part of the filter is more uniform as there is no effect of the
lamp in that region. With increasing the flow rate, the relative velocity
distribution (regardless of its magnitude) is almost the same, and the
flow tends to pass below the lamp. In the contour plots (Fig. 5), it can be
pointed out that the magnitudes of velocity on the filter media corre-
sponding to the lamp location are nearly identical for all the considered
flow rates, and the main variation can be observed in the area below the
lamp.
The CFD simulation results indicated that the expansion and re-
duction in the geometry as well as the presence of lamps at the middle
part, cause a significant flow mixing in the channel, resulting in the
non-uniform flow in the PCO reactor. Although the streamlines behind
the wire mesh become more uniform, they deviate when the flow is
close to the lamps and also behind the lamps, where the PCO filter is
placed, leading to the non-uniform flow in the PCO filter.
In the next step, results from the simulation of the tracer gas were
compared with experimental data. For this purpose, distribution func-
tions E(t) were plotted versus time using the CO2 outlet concentration
and applying Eq. (2). The RTD experiment was also performed, and the
concentration of CO2 tracer was measured with the flow rate of 10 L/
min lasting 224 s both in the presence and in the absence of the pho-
tocatalyst media (see Fig. 6-a). It can be observed from this figure that
the results of the residence time distribution in the PCO reactor for the
experiment including the filter, are very similar to those gained in the
experiment without the filter. This can be justified and attributed to the
fact that the SFF filter is highly porous ( =ε 0.9628), and the non-ad-
sorbing gas (CO2) can easily pass through it. Further, the results ob-
tained from the numerical simulation are in good agreement with the
experimental one. This indicates that this simulation approach can be
used to predict the flow behavior, even in complex geometries, and
with high accuracy. The simulations were also performed for the as-
sumption of ideal plug flow and laminar flow to investigate deviations
with respect to the actual flow. Fig. 6-b confirms that the dispersion in
the PCO reactor is not negligible, as the RTD curve for the actual flow is
fairly different from those of ideal flows. In the case of plug flow,
molecules have the same residence time and move with the same ve-
locity and concentration. However, in the laminar flow, molecules in
the centerline of the reactor channel move faster than those near the
Table 2
Physical properties of TiO2/SFF filter.
Parameter PCO filter
Fiber diameter 10 µm
Specific surface area (BET) 150.8 m2/g
Bed porosity 96.28
TiO2 layer thickness 1 µm
Filter thickness 3–5 mm
a cb
Fig. 2. SEM images of TiO2/SFF filter at different magnifications.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
5
wall (as the velocity profile of laminar flow is parabolic), which leads to
a higher dispersion than in the case of plug flow. Fig. 6-c displays that
with increasing flow rate up to 40 L/min, dispersion decreases. How-
ever, there is a considerable deviation from ideal plug flow and laminar
flow. It should be mentioned that the results in Fig. 6 determined in a
way that the area under the E(t) curve of RTD is unity. The analytical
model displayed in this figure will further be explained in Section 3.2.
3.2. Analytical analysis of RTD
Users of photocatalysts generally do not have access nor knowledge
of CFD tools. Thus, one of the aims of this research is to develop a
simple and straightforward methodology for the evaluation of flow
characteristics in the presence of dispersion using the RTD curve. To
characterize the non-ideal flow within reactors, several models have
been developed, namely, continuous stirred tank reactors in series and
dispersion models [38,39].
Since RTD data are generally known for a number of discrete time
intervals, the mean residence time (t̄m) and the variance of the residence
time (σ2) can be evaluated as [38]:
= ∫ =
∑
∑
∞ ∞
∞t tE t dt
t C t t
C t t
¯ ( )
( )Δ
( )Δm
i i i
i i0
0
0 (3)
=
∫ −
∫
=
∑ −
∑
∞
∞
∞
∞σ
t t C t dt
C t dt
t t C t t
C t t
( ¯ ) ( )
( )
( ¯ ) ( )Δ
( )Δ
m i m i i
i i
2 0
2
0
0
2
0 (4)
The axial dispersed plug flow model, or simply the dispersion model
has been applied to simulate the non-ideal behavior of the gas in the
PCO reactor. Considering the fact that the axial dispersion is mainly due
to velocity gradients whereas the lateral dispersion is owing to the
molecular diffusion only [38], the differential equation representing
this dispersion can be expressed as:
∂
∂
= ∂
∂
− ∂
∂
C
t
D C
x
u C
xax
2
2 (5)
where Dax is the axial dispersion coefficient, which characterizes the
degree of dispersion. It should be noticed that the concentration gra-
dient in lateral directions was assumed to be negligible. By considering
an opened-opened vessel, the analytical solution of the model can be
described as follows [38]:
= − −E t u
πD t
L ut
D t
( )
4
exp[ ( )
4
]
ax ax
2
(6)
= = + =−σ
σ
t Pe Pe
Pe uL
D
2 8 withθ
m ax
2
2
2 (7)
where L, u and Pe represent the characteristic
length, the superficial
velocity, and the Peclet number, respectively. By applying the proposed
method for the CO2 tracer, the result is demonstrated in Fig. 6. It can be
observed that the analytical solution perfectly matches the experi-
mental result. This method was then used to evaluate the RTD analysis
of MEK at various flow rates. Fig. 7-a presents the residence time dis-
tribution behavior of the PCO reactor and simulation results gained
with the use of the axial dispersion model at flow rates of 10, 20, 30, 40,
50, 60 L/min. It was found that, with an increase in the airflow rate, the
peak value of the tracer increases as well. Moreover, the higher the flow
rate, the shorter the time after which the peak was observed. Thus, the
dispersion decreases with enhancing the flow rate, which is in ac-
cordance with the earlier investigations [23,40,41]. As Peclet number
Fig. 3. Schematic of the experimental set-up for RTD experiments.
Fig. 4. CFD modeling of the fluid field in the reactor channel at Q = 10 L/min (red lines show the streamlines). (For interpretation of the references to colour in this
figure legend, the reader is referred to the web version of this article.)
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
6
indicates the extent of axial dispersion, it was plotted versus velocity in
Fig. 7-b. Under our experimental conditions, the Pe value is lower than
100, which is the acceptable minimum limit for plug-flow [38]. These
low values of Pe imply that the PCO reactor cannot be considered as an
ideal plug-flow reactor owing to that substantial axial dispersion. On
the other hand, it easy to see that the axial dispersion coefficient (Dax)
continuously increases as superficial velocity increases (see Fig. 7-b). As
the value of Re.Sc in the present study is between 200 and 1000, the
axial dispersion coefficient, according to the Aris-Taylor correlation
[42,43], can be represented by a quadratic function of the superficial
velocity (Dax = αu2) [38]. However, the correlation proposed by Aris-
Taylor is only valid for cylindrical channels.
In this work, the best fit is given by:
=D u2.207ax 2 (8)
3.3. PCO reaction under mass transfer limitation
The performance of the PCO system was assessed based on the re-
moval efficiency of the MEK in the gas phase. The single-pass removal
efficiency of the PCO filter was evaluated as follows:
= = − ×C C
C
Removal efficiency (%) X ( ) 100in out
in (9)
where Cin and Cout are the upstream and downstream concentrations in
a steady-state condition, respectively. Fig. 8 demonstrates the removal
efficiency of MEK versus light intensity and flow rate for two different
PCO filter thicknesses. As it is mentioned before, the reaction requires
to be conducted at shorter filter thickness and high lamp radiation to
ensure that the system operates at the mass transfer-controlled regime.
This way, it was assured that the lights with high intensities could
completely penetrate the media, resulting in an extremely active pho-
tocatalyst. Therefore, to determine the optimum value the photo-
catalysis reaction experiment was performed at various light intensities
(Fig. 8-a). This figure shows that the optimum point for both filters was
at a light intensity of 78 mW/cm2. It should be noted that, to reach high
conversion under the mass transfer-limited condition, all experiments
were performed at a low concentration of MEK (150 ppb). In Fig. 8, at
lower light intensity, filter with a thickness of 3 mm has higher removal
efficiency, whereas, at high light intensity, it has lower efficiency
compared to the filter with 5 mm thickness. This can be attributed to
the possibility of the electron-hole recombination in the thick photo-
catalyst [44]. However, with elevating the light intensity, the number
Fig. 5. Contours and distribution of the velocity magnitude at the PCO filter cross-section for various flow rates; (a) Q = 10 L/min, (b) Q = 20 L/min, (c) Q = 30 L/
min, (d) Q = 40 L/min.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
7
of activated particles in the filter with 5 mm thickness increases, which
leads to outperform the other one.
Fig. 8-b demonstrates the dependence of the experimentally mea-
sured MEK conversions upon flow rate. The experimental light intensity
was taken equal to 78 mW/cm2 when the apparent reaction rate is
completely controlled by mass transfer limitations. As expected, for all
samples, the observed removal efficiency decreases as flow rate
increases (due to the corresponding reduction of the residence time).
The mass balance through the PCO filter considering axially dis-
persed plug flow and steady-state condition and assuming a pseudo-
first-order reaction is given by:
− − − − =D d C
dx
u dC
dx
ε
ε
k a C C(1 ) ( ) 0ax b
m ext
s s
2
2 , (10)
= − =r k a C C k C( )m ext s s app s, (11)
where km ext, , as, ε, Cs, r and kapp are the external mass transfer coeffi-
cient, the geometric surface area per unit volume, the bed porosity,
VOC concentration at the catalyst phase, the photocatalysis reaction
rate, and the apparent photodegradation rate constant, respectively. In
the case of a high reagent consumption in comparison with the mass-
transfer process, a significant concentration gradient happens in the
boundary layer. It means the surface reaction is extremely rapid, and
the mass transfer rate to the surface dictates the overall rate of reaction.
Accordingly, the concentration Cs becomes much lower than the bulk-
gas concentration (i.e., ≪C Cs ) [45]. Eqs. (10) and (11) are readily
combined to give:
− − − =D d C
dx
u dC
dx
ε
ε
k C(1 ) 0ax b ov
2
2 (12)
where the overall rate constant (kov) is stated as:
= + =
k k k
k k a1 1 1 with
ov mt app
mt m ext s,
(13)
Since mass transfer is the rate-controlling process ( ≫k kapp mt), then
≈k kov mt . To solve the Eq. (12), Danckwert’s boundary conditions were
applied as:
Fig. 6. Residence time distribution E(t) of CO2 in the PCO reactor; (a) the
comparison between simulation and experimental results in the presence/ab-
sence of catalyst (b) the deviation of the actual flow from the ideal plug flow
and the laminar flow at Q = 10 L/min (c) the deviation of the actual flow from
the ideal plug flow and the laminar flow at Q = 40 L/min determined by a
simulation.
Fig. 7. (a) The residence time distribution E(t) of MEK at various flow rates, (b)
the dependence of the Peclet number and axial dispersion values on the su-
perficial velocity.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
8
= − =u C u C D dC
dx
xat 0b in b ax (14)
= =dC
dx
at x L0 f (15)
The analytical solution of Eq. (12) in term of removal efficiency (Eq.
(9)) can be written as [38]:
= − = −
+ − − −( )
X C
C
qexp
q q
1 1
4 ( )
(1 ) exp (1 ) exp( )
out
in
u L
D
qu L
D
qu L
D
2
2
2
2
2
b f
ax
b f
ax
b f
ax (16)
The parameter q is expressed as:
= +
−
q
k a τD ε
u L ε
1
4 (1 )m ext s ax
b f
,
(17)
where τ , and Lf are the hydraulic residence time of reactor (s) and
thickness of SFF filter, respectively. The geometric surface area as (m2/
m3) was calculated on the basis of fiber diameter and coating thickness
(shown in Fig. 9) through Eq. (18).
=
+
+ −
=
+
+( )
( )
( ) ( )
a
π δ L
π δ L
d δ
dδ δ
2 2
s
d
f fb
d
f
d
fb
f
f f
2
2
2
2
2 2
(18)
where d, δf and Lfbrepresent fiber diameter, the TiO2 layer thickness,
and the fiber length, respectively. For the SFF filter used in this study, a
value of 109 × 103 (m2/m3) was calculated based on SEM analysis (see
Table 2).
The relevant variables were then expressed in dimensionless form
by calculating the Sherwood (Sh), Schmidt (Sc), and Reynolds (Re)
numbers, as defined in the Nomenclature section. For the range of ex-
perimental conditions, Sc was calculated to be 1.04. Using this value of
Sc, Sh is calculated based on the mass transfer coefficients obtained for
two different catalyst thicknesses and plotted against Re, as shown in
Fig. 10. This figure displays
that Sh number for airflow rate ranging
from 10 L/min to 40 L/min using thickness of L = 3 mm is very close to
L = 5 mm. This indicates that mas transfer is independent of the cat-
alyst bed thicknesses due to the same geometry and characteristic of the
fibrous catalyst. Following correlation was obtained using least squares
regression:
=Sh Re Sc0.0056 0.4663 13 (19)
where Re is defined based on fiber diameter and interstitial velocity.
Due to very small fiber diameters, Re becomes lower than unity in the
SFF filter. Correspondingly, the observed dimensionless mass transfer
coefficients are very low.
Contrary to earlier works on fiber-based structured materials, which
focused more on the activity of the catalyst, limited numbers of articles
covering mass transfer are available [27]. To date, just a few correla-
tions between Sherwood and Reynolds numbers for fibrous catalyst in
the gas phase with low Reynolds number are available. Table 3 de-
monstrates some literature correlations for mass transfer in fiber-based
catalyst supports (except Ref. [46]; for monolith structure) validated for
the relatively low range of Reynolds number. Groppi et al. [47] studied
the gas/solid mass transfer in metallic fiber filter. Their results showed
significantly low values for Sh number. Satterfield [48] and Ahlstrom-
Silversand [49] studied the mass transfer characteristics of wire-mesh
catalysts with high porosity and then proposed correlations for the mass
transfer coefficient in absent of axial dispersion. The correlation pro-
posed by Votruba [46] for the monolithic structure was commonly used
in PCO studies [3,25,50]. Zhong [3] used Votruba’s correlation to
evaluate mass transfer coefficient of fiberglass filter by considering fiber
diameter as the characteristic length. However, this correlation was
obtained based on mass transfer through the vaporization of liquid from
the surface of monolithic structure. Furthermore, in Votruba’s correla-
tion, hole diameter of the monolith was defined as characteristic length.
Fig. 11 compares the correlation developed in the present study
with those given in the literature for 0.01 < Re < 10 at a constant
Sc = 1.04. At low values of Re, prediction by Groppi is closer to the
present study. However, the deviation increases when it is compared
with other ones. By increasing the value of Re, the calculated Sh
number of all other correlations deviated considerably from that of the
present study. One of the possible explanations for higher deviation is
the effect of axial dispersion on mass transfer, which was neglected for
studies related to wire mesh and honeycomb type of catalyst (i.e. Refs.
[46,48,49]). Although Groppi accounted the axial dispersion effect for
developing the mass transfer equation, the correlation demonstrates a
weaker dependence on Re than that of present work. Groppi’s corre-
lation was validated for lower porosity and higher fiber diameter,
which over predicts the mass transfer for the condition related to the
present study. Correlations related to wire mesh (i.e. Satterfield and
Ahlstrom-Silversand) are validated for high Re number where turbu-
lences may occur. Votruba obtained the relationship by considering the
hydraulic diameter of the monolith as the characteristic length, which
may cause such a significant deviation [46].
Fig. 8. MEK PCO efficiency as a function of (a) light intensity (flow
rate = 10 L/min) (b) flow rate (intensity = 78 mW/cm2).
Fig. 9. Schematic of a silica fiber coated with TiO2.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
9
The above observations highlight the necessity for the verification
and assessment of the applicability of mass transfer correlations for
actual conditions prior to their use for the performance estimation.
4. Conclusion
Experimental and simulation study of the ultraviolet photocatalytic
oxidation (UV-PCO) reactor was carried out considering the presence of
mass transfer limitation and axial dispersion.
A three-dimensional CFD model was developed to simulate flow
characteristics in the reactor. Simulation results for different flow rates
showed that the UV lamp had a major impact on the flow distribution at
the catalyst surface. It was found that with increasing the inlet flow
rate, the velocity distribution (regardless of its magnitude) was almost
identical. A tracer gas study with a signal injection of CO2 was con-
ducted to determine the residence time distribution (RTD) in the re-
actor, and good agreement between experimental and simulation re-
sults was observed.
Furthermore, a quick and straightforward methodology employing
an axial dispersion plug flow model was proposed to characterize the
flow through the RTD analysis. First, results obtained in the RTD ana-
lysis of CO2 were compared with experimental one and with the one
made by the CFD model. Owing to the high porosity of the filter
( =ε 0.9628), the RTD of CO2 in the presence and absence of the filter
was almost identical. Further, the proposed model was used to evaluate
the axial dispersion coefficient of methyl ethyl ketone (MEK) at dif-
ferent flow rates through the reactor. A quadratic function was used to
correlate the axial dispersion coefficient with the superficial velocity.
The axial dispersion coefficient increased progressively with the in-
crease of the superficial velocity. Due to a low value of the Peclet
number (Pe < 100), indicating the extent of axial dispersion, the flow
in the reactor could not be considered as an ideal plug flow reactor as a
considerable dispersion took place in the reactor.
A steady-state mass balance equation was utilized for the descrip-
tion of mass transfer limitation and axial dispersion in the reactor. A
photocatalysis reaction experiment with a silica-fiber-felt (SFF) filter
and MEK (as a challenging compound) was performed. In the experi-
ment, a short filter thicknesses and high light intensity were applied to
ensure that the system operated at the mass-transfer-controlled regime.
Since the reaction rate was extremely high, the resistance to the PCO
reaction is negligible in comparison with the mass transfer resistance,
accordingly, the overall rate constant was considered identical to the
mass transfer coefficient. The mass transfer coefficient was calculated
with the use of the proposed model and an empirical correlation for the
Sherwood number was proposed. The comparison of the proposed
formula with other available correlations indicated that all these cor-
relations adopted from the literature overestimated the mass transfer
coefficient in cases with low Reynolds numbers 0.01 < Re < 10. The
reason is that other correlations were validated for relatively high
Reynolds number and also in most of the correlations, dispersion effect
was neglected.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Acknowledgment
The authors would like to express their gratitude to Concordia
University, Canada for support through the Concordia Research Chair-
Energy & Environment. Dr. Klimes’s participation was supported by
ComSi (No. CZ.02.1.01/0.0/0.0/16_026/0008392) by OP RDE (ERDF).
Fig. 10. Dependence of the Sh number upon the Re number in SFF filter with
varying thickness and velocity (Sc = 1.04).
Table 3
Experimental parameters and correlations used in different research works.
Application Study Media type ε d(μm) Re Pe Correlation
Photocatalytic reaction Present work Fiberglass 0.9628 10 0.02–0.07 8–17 =Sh Re Sc0.0059 0.4663
1
3
Catalytic reaction Groppi [47] Metal fiber 0.86 25 0.25–1 >10 =Sh Re Sc0.089 0.72
1
3
Satterfield [48] Wire mesh 0.71–0.91 68.5–84 1–100 very high =Sh Re Sc0.47 0.283
1
3
Ahlstrom-Silversand [49] Wire mesh > 0.7 300–1650 0.8–140 very high =Sh Re Sc0.78 0.45
1
3
Liquid vaporization Votruba [46] Honeycomb 0.32–0.38 1–10× 103 3–480 very high
⎜ ⎟= ⎛
⎝
⎞
⎠
Sh Re Sc0.705 d
Lf
0.43
0.56
Fig. 11. Effect of Re on Sh as predicted by various correlations at Sc = 1.04.
M. Malayeri, et al. Chemical Engineering Journal 386 (2020) 124013
10
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.cej.2020.124013.
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	Modeling of gas-phase heterogeneous photocatalytic oxidation reactor in the presence of mass transfer limitation and axial dispersion
	Introduction
	Methodology
	Experimental setup
	Analysis instruments
	Modeling with COMSOL Multiphysics
	Material
	Residence time distribution experiment
	Mass-transfer limited PCO experiment
	Result and discussion
	CFD simulations
	Analytical analysis of RTD
	PCO reaction under mass transfer limitation
	Conclusion
	mk:H1_14
	Acknowledgment
Supplementary data
	References